What is the difference between human brains and neural networks?
One incredibly important difference between humans and NNs is that the human brain is the result of billions of years of evolution whereas NNs were partially inspired by looking at the result and thinking "... we could do that" (utmost respect for Hubel and Wiesel).

Human brains (and in fact anything biological really) have an embedded structure to them within the DNA of the animal. DNA has about 4 MB of data and incredibly contains the information of where arms go, where to put sensors and in what density, how to initialize neural structures, the chemical balances that drive neural activation, memory architecture, and learning mechanisms among many many other things. This is phenomenal. Note, the placement of neurons and their connections isn't encoded in dna, rather the rules dictating how these connections form is. This is fundamentally different from simply saying "there are 3 conv layers then 2 fully connected layers...". 
There has been some progress at neural evolution that I highly recommend checking out which is promising though.

Another important difference is that during "runtime" (lol), human brains (and other biological neural nets) have a multitude of functions beyond the neurons. Things like Glial cells. There are about 3.7 Glial cells for every neuron in your body. They are a supportive cell in the central nervous system that surround neurons and provide support for and insulation between them and trim dead neurons. This maintenance is continuous update for neural structures and allows resources to be utilized most effectively. With fMRIs, neurologists are only beginning to understand the how these small changes affect brains. 

This isn't to say that its impossible to have an artificial NN that can have the same high level capabilities as a human. Its just that there is a lot that is missing from our current models. Its like we are trying to replicate the sun with a campfire but heck, they are both warm.